A lifting surface is defined as a surface which, due to the relative motion of a fluid such as an air across its surface, provides a positive force on one of the surfaces which can then be transmitted to the conveyance in form of a motion.
As an illustration of a lifting surface, an aircraft wing is a lifting surface. Likewise a keel on a sailboat is a lifting surface. Sails for boats are most commonly known as pliant lifting surfaces. Typically, the sails on a sailboat are a jib or a Genoa sail, a mainsail, and other sails such as mizzen sails for ketches and yawls. Other sails are trysails, staysails, spinnakers, and various other types where the force imposed by the wind on the sail is borne by a pliant fabric or a pliant plastic and fabric laminate such as a plastic reinforced with a scrim or a fabric (on one or both sides of the plastic sheet). As the sail material bears all the exerted forces, its weave, construction, fabric orientation, and reinforcement aspects are critical.
In order to have a lifting surface of a maximum efficiency such as for a sailboat and especially for a sailboat engaged in competitive racing, it is important that for any given wind conditions the lifting surface is not irreversibly distorted due to the distortion in the pliant material itself such as in the fabric or plastic sheet or plastic sheet and fabric composites.
Hence, the appropriate fabric must be selected for each of the given conditions for which the sail is anticipated to be used. Furthermore, the plastic laminate must also be especially carefully reinforced so that it does not distort beyond a given point. A plastic laminate is generally reinforced with a scrim throughout its entire body or the laminate consists of fabric on either one or both sides of the plastic such as in a sandwich construction.
Typically, before the onset of laminated sails, these were made of a woven fabric. If a woven material is used, the woven material has all the characteristics typically found in such material. That is, the woven material has warp and weft threads. Woven material has poor bias properties. Plastic laminates have better bias properties.
For each type of threads used for a woven material, these may be made of different or the same material. Different threads impart different characteristics to the fabric, such as different tensile strength or failure mode characteristics. In order to accomodate differences in the warp and weft and bias behavior, the fabric is aligned in such a manner as to take the most stress along warp lines, i.e., the lines where the stress is imposed on the sail.
The forces or loads on a sail and its fabric are exerted in a complex manner. These loads may be described by various notations, e.g., as contour lines, or lines of equal forces or load cells exerted on the sail. It must be understood that load lines are approximations and are done for convenience because the force is substantially solely, in the typical prior art sail, transmitted by the pliant fabric. The force is transmitted in an uneven fashion on a sail which is a surface of complex compound curves. For this complex curve surface, it is important that the surface has the right shape, because the maximum lifting efficiency over long periods of time has been developed as an art merely by comparison to a previous sail or a sail with given performance characteristics.
In addition, each of the sails must also have some relationship to the vehicle being driven, such as a sailboat or an iceboat. For the last, because of the tremendous speeds being achieved by these boats, i.e., in excess of 80 mph, sails must have a different shape from one that is typically being sailed at very low speeds, for example, less than five mph.
Moreover, the load distribution on these two lifting surfaces varies considerably. Sailmaking over the past has been an art which has relied on the proper shaping of the various component parts in the sail to obtain the surface. However, it is emphasized that substantially entirely the forces or loads have been borne by the skin, i.e., the fabric that forms the lifting surface.
For ease of description herein, the sail will be designed as consisting of a head, that is, the upper part of it to which a halyard is attached to hoist the sail up the mast or up a head stay. The bottom of the sail is attached at the front part thereof by its tack to the boat; and, at the aft part, the sail is attached by its clew either to a boom or a sheet. These sails may also be free-flying or be carried in a luff groove. Sails may also be attached to a head stay or a mast by hanks or slides, respectively. These are at intermittent positions along the luff of the sail.
A sail has a foot which is the bottom part of the sail and a leech, the aft part of the sail. The part of the sail projecting beyond the straight line between the head of the sail and a clew is called a roach and the line itself a roach line. The part short of the roach line is called a hallow. The sail curvature or projection between any point on the luff and a roach (parallel to the water) is called a camber. Further, the aspect ratio of the sail is expressed for a triangular sail as the height (or length) of the sail squared divided by the sail area of the sail. Aspect ratio is an important consideration for modern racing sails.
The aerodynamic force on the sail is expressed generally as: EQU F=0.00119.times.v.sub.a.sup.2 .times.S.sub.a .times.C,
where F is the aerodynamic force in pounds, v.sub.a is the velocity of the apparent wind in feet per second, and S.sub.a is the sail area in square feet. C is the aerodynamic force coefficient for a given sail.
Expressed in another manner, for a full-size sail the force is referred to as: EQU .sup.F tf.s=C.sub.t .times.0.00119v.sub.a.sup.2 f.s.times.Safs,
where fs stands for full-sized, and F.sub.t stands for total force. The total lift, load, or the force thus are equivalent.
However, each of the sail shapes has its own coefficient C.sub.t and its own load bearing characteristics. The forces are a resultant of the various forces or loads induced on the lifting surface by the aerodynamic flow and drag of air over the surface.
If the force exerted on any particular area on the sail is measured and then the areas which have equal force exerted on these are joined by a line, an equal force contour line on the sail may thus be defined. Appropriately defined increments in the force contour lines will then show the equal force distribution over the surface of the sail.
These contour lines approximate the stresses which are being imposed on the sail, as distorted or further amplified based on the point loads or stresses at boundary supports. At points of loading, e.g., attachment points of the sail, the forces or loads are being transmitted to the rigid structure, such as a sailboat. At these points the loads are especially severe.
These concepts are explained such as by Marchaj, Sailing Theory and Practice, Dodd, Mead and Company, New York, 1964. A distribution of the pressure on a sail has been illustrated such as on page 59 of the above-mentioned book.
Because of the very complex compound curves for the sail or the lifting surface, there is very little data available for each of the particular sails. If it is taken into account that the support points or point loads such as the head, the clew, and the tack concentrate the force contour lines, it is seen that the various attachment points have very high stress areas.
For modern high aspect sails, the forces such as at a clew or at a head are very high. Attachment points are strengthened in a traditional sail by reinforcement patches of various constructions and types.
In addition, if sail slides, hanks or reef tacks or clews are further taken into account, it is seen that the force distribution over the surface area is complex.
These forces, of course, as seen from the above formula, vary as the wind velocity varies with the force increasing as a square with each increase in the linear wind speed measured either as feet per second or meters per second or whatever system is being used.
Accordingly, the sail has to accomodate to the best lifting surface conditions by an appropriate shape built into it and appropriate adjustments which are being made to the sail for the various conditions encountered. Thus at any given wind angle of attack the force contours as well as the magnitude thereof will also vary over the sail surface. Hence, the sail coefficient C.sub.t will vary in the above formula. For well-made sails or well-adjusted sails, the value for C.sub.t will be larger than for poorly made sails and poorly adjusted sails.
In general, the three principal directions of sailing in a sailboat based on the angle of attack of the sail vis-a-vis the wind are: beating, reaching and running. The highest load on a sail for a given true wind strength is imposed when the boat is in its beating mode. Hence, the forces are again different based on the angle of attack to the wind. The shape of the sail for each condition must be changed in order to obtain the best lifting surface characteristics.
The lifting surface characteristics are controlled by the sheet tension, the halyard tension, the sheet lead angles with respect to the tack position, the tension on the luff such as may be exerted by a halyard tension or a Cunningham line tension or on the foot, such as may be exerted by changing the sheet lead and/or sheet tension position or the outhaul position (outhaul tension) such as on a boom. Further, sails are often reefed, i.e., sail area and shape are changed, such as by a flattening reef, or a mast is bent to change the shape of the sail to either "up-power" or "down-power" the sail for any given wind condition. Places where the reef points are located must also have reinforcements, and these introduce again different force contour lines when the sail is reefed.
As the adjustments in the various control lines are being made for optimum sailing conditions, the force contour line changes. These force contour lines are affected further as a result of the dynamic loading (as opposed to the static loading) in a seaway or due to the pitching or yawing of the boat and in a gust-and-lull sailing condition. These sail force contour lines, as it is seen, are not static, but move around the surface of the sail and affect the efficiency of the sail and therefore the hull being driven by the sail.
Other factors that influence the sail efficiency are such as mast and standing rigging motion, as well as weight aloft. As it concerns the weight aloft, this matter will be treated further in the discussion of the novel construction disclosed herein.
Still further, the apparent and true wind concept is also of great significance. In boats that often sail in smooth water where the dynamic loading is not greatly affecting speed, large boats or small boats such as iceboats can achieve speeds in excess of the true wind and thus as the wind force increases due to the relative or the apparent wind vis-a-vis the true wind, the forces on the sail increase appropriately as shown by the above formula. This concept is also known by a shorthand expression of "making its own wind", and is especially noticeable for iceboats.
Because a given lifting surface is generally useful over a fairly narrow range, the sail must be constructed for fairly narrow wind ranges and wind conditions.
Consequently, because of the distortions and irreversible distortions when a sail has been overstressed, the restrictions on the wind speed are especially severe when the laminate sails are being used. Laminated sails distort precipitously beyond a yield point and the sail then loses its efficient lifting surface characteristics or is totally destroyed.
As a consequence, modern backing fabrics have been employed to stabilize the laminate film, and the modern laminates consist predominantly of Mylar film with Dacron reinforcements and Mylar film with Kevlar reinforcements. Mylar is a film and Dacron is a fabrich thread material of a polyester polymer. Mylar and Dacron are trademark of the Dupont Company. Kevlar is an aramid polymer, and Kevlar is also a trademark of the Dupont Company. Thus the Dacron and Kevlar fabrics and reinforcements made from these materials have the essential function of stabilizing the laminated sail material as the forces are being imposed on the sail fabric or laminate.
In a similar manner, the Kevlar and Kevlar laminates (aramid polymers and the derivatives of the aramid family) are being increasingly used because the Kevlar material possesses extremely advantageous strength to weight ratios. Reduction of weight aloft is important to reduce the pitching and yawing motion and the dynamic loading of a sail.
With less weight aloft, a boat pitches and yaws less, and therefore has a more efficient forward force. However, the reduction of the weight is at the increase of the risk of distorting the sail. As a result, the trade-offs in these areas become extremely complex and are further exacerbated because the sail is generally, for want of a better description, designed for narrow apparent wind speed ranges of less than 14 mph, from 14 to 22 mph and above 22 mph, and designated as useful for light, medium and heavy air conditions. Hence, sails are conventionally made of an appropriate size and design to accomodate these wind speeds.
Because of the extremely complex interaction of forces, for a full-size sail, stress magnitude calculations, however, are merely approximations. Consequently, appropriate safety factors used are generally expressed as an upper permissible wind speed at which the sail can be used before damage to the sail fabric occurs. Damage generally occurs along the seams of the material in the fabric itself.
As the reduction of the weight is at the increased risk of distorting the sail, the trade-offs in these areas, as mentioned above, become extremely complex and are exacerbated by economic factors because the price of Kevlar-Mylar laminates is comparatively high to the modern fabrics made solely of Dacron fabric with conventional warp and weft yarns. However, the disadvantage of the warp and weft orientation is that these sails have very little bias strength.
This lack of bias strength again translates into distorted sails. For this reason, the laminates of the Mylar and Dacron and Mylar and Kevlar eliminate some of the bias distortions, primarily because the Mylar films have strength characteristics which prevent this bias distortion to a considerable degree.
However, these fabrics have disadvantages, e.g., sails made of Kevlar. Kevlar's flexure properties are considerably poorer compared with Dacron sails. Thus flogging destroys the Kevlar fibers, i.e., fabric, because its flexure life is considerably poorer as compared with Dacron. Moreover, flogging of a sail is especially damaging at high wind speeds. Again, these factors introduce trade-offs where the outstanding strength for Kevlar is at a sacrifice due to its flexure-life properties, i.e., useful sail life.
As a result of the new introduction of the more effective strength-to-weight materials such as Kevlar, there has been a continuous development of sails which ostensibly accomodate the various load distribution in a sail. These attempts are aptly illustrated by the sails shown such as in Yacht Racing and Cruising, Vol. 23, No. 11, 1984, captioned Sailboats '85. For example, the sails shown on pages 8a-b, 149, 155 and 157-9 illustrate the high intensity of the design effort. As it is evident from the various shapes illustrated in this publication, there has been a constant striving to devise a stress or load bearing sail of an improved fabric orientation for the load borne by the skin, i.e., fabric. These attempts have been made by using various fabric characteristics and the various strength properties of the fabric or thread materials.